Short post comparing Projective Geometric Algebra and Conformal Geometric Algebra for the simple problem of line-sphere intersection:

Source

• URL: https://x.com/hamish_todd/status/1804130765296263172
• Author: Hamish Todd (@hamish_todd)
• Posted: 2024-06-21 12:34:28

Thread

1/ @hamish_todd

Short post comparing Projective Geometric Algebra and Conformal Geometric Algebra for the simple problem of line-sphere intersection:
https://hamishtodd1.substack.com/p/line-sphere-intersection-in-projective?r=hhpio&utm_campaign=post&utm_medium=web&showWelcomeOnShare=true&triedRedirect=true

2/ @EricLengyel

@hamish_todd

That method of point extraction in the CGA case is outdated.

3/ @EricLengyel

Also, your calculation of d² gives the negative squared radius in the CGA case, so there’s no intersection when it’s positive, and you need to negate it before taking the square root.

4/ @EricLengyel

@hamish_todd

Also also, using the geometric product to calculate the squared radius is overkill and generates 5 unnecessary terms. Use the much simpler inner product instead.

Branches: 2024-06-22-hamish_todd-will-correct-this-in-the-morning-thanks